A shock absorbing device described in JP2006-336816A and JP2007-78004A includes a cylinder, a piston that is inserted into the cylinder to be free to slide and partitions the interior of the cylinder into an upper chamber and a lower chamber, a first flow passage provided in the piston to connect the upper chamber and the lower chamber, a second flow passage that opens onto a side portion of a piston rod from a tip end thereof and connects the upper chamber and the lower chamber, a housing that is attached to the tip end of the piston rod and includes a pressure chamber connected to a midway point of the second flow passage, a free piston that is inserted into the pressure chamber to be free to slide and partitions the pressure chamber into a one chamber and the other chamber, and a coil spring that biases the free piston. Thus, the one chamber of the pressure chamber communicates with the lower chamber via the second flow passage and the other chamber of the pressure chamber communicates with the upper chamber via the second flow passage.
In the shock absorbing device described above, the pressure chamber is partitioned into the one chamber and the other chamber by the free piston, and therefore the upper chamber and the lower chamber do not communicate directly via the second flow passage. However, when the free piston moves, a volume ratio between the one chamber and the other chamber varies such that a liquid in the pressure chamber travels between the upper chamber and the lower chamber in accordance with a movement amount of the free piston, and therefore it appears as if the upper chamber and the lower chamber are connected via the second flow passage.
Here, when a differential pressure between the upper chamber and the lower chamber during expansion and contraction of the shock absorbing device is set as P, a flow rate of liquid flowing out from the upper chamber is set as Q, a coefficient expressing a relationship between the differential pressure P and a flow rate Q1 of liquid passing through the first flow passage is set as C1, a pressure in the other chamber of the pressure chamber is set as P1, a coefficient expressing a relationship between a difference between the differential pressure P and the pressure P1 and a flow rate Q2 of liquid flowing into the other chamber of the pressure chamber from the upper chamber is set as C2, a pressure in the one chamber of the pressure chamber is set as P2, a coefficient expressing a relationship between the pressure P2 and a flow rate Q2 of liquid flowing into the lower chamber from the one chamber is set as C3, a sectional area serving as a pressure receiving surface area of the free piston is set as A, a displacement of the free piston relative to the pressure chamber is set as X, and a spring constant of the coil spring is set as K, and a transfer function of the differential pressure P relative to the flow rate Q is determined, Equation (1) is obtained. It should be noted that in Equation (1), s denotes a Laplace operator.
                              G          ⁡                      (            s            )                          =                                            P              ⁡                              (                s                )                                                    Q              ⁡                              (                s                )                                              =                                    C              ⁢                                                          ⁢              1              ⁢                              {                                  1                  +                                                                                    A                        2                                            ⁡                                              (                                                                              C                            ⁢                                                                                                                  ⁢                            2                                                    +                                                      C                            ⁢                                                                                                                  ⁢                            3                                                                          )                                                              ⁢                                          s                      /                      K                                                                      }                                                    1              +                                                                    A                    2                                    ⁡                                      (                                                                  C                        ⁢                                                                                                  ⁢                        1                                            +                                              C                        ⁢                                                                                                  ⁢                        2                                            +                                              C                        ⁢                                                                                                  ⁢                        3                                                              )                                                  ⁢                                  s                  /                  K                                                                                        (        1        )            
Further, when jω is substituted for the Laplace operator s in the transfer function shown in Equation (1) and an absolute value of a frequency transfer function G (jω) is determined, Equation (2) is obtained.
                                                    G            ⁡                          (              jω              )                                                =                                                                              C                  ⁢                                                                          ⁢                                      1                    [                                                                  K                        4                                            +                                                                        K                          2                                                ⁢                                                  A                          4                                                ⁢                                                  {                                                                                    2                              ⁢                                                              (                                                                                                      C                                    ⁢                                                                                                                                                  ⁢                                    2                                                                    +                                                                      C                                    ⁢                                                                                                                                                  ⁢                                    3                                                                                                  )                                                            ⁢                                                              (                                                                                                      C                                    ⁢                                                                                                                                                  ⁢                                    1                                                                    +                                                                      C                                    ⁢                                                                                                                                                  ⁢                                    2                                                                    +                                                                      C                                    ⁢                                                                                                                                                  ⁢                                    3                                                                                                  )                                                                                      +                                                          C                              ⁢                                                                                                                          ⁢                                                              1                                2                                                                                                              }                                                ⁢                                                  ω                          2                                                                    +                                                                                                                                                                                                                                                                    A                            8                                                    ⁡                                                      (                                                                                          C                                ⁢                                                                                                                                  ⁢                                2                                                            +                                                              C                                ⁢                                                                                                                                  ⁢                                3                                                                                      )                                                                          2                                            ⁢                                                                        (                                                                                    C                              ⁢                                                                                                                          ⁢                              1                                                        +                                                          C                              ⁢                                                                                                                          ⁢                              2                                                        +                                                          C                              ⁢                                                                                                                          ⁢                              3                                                                                )                                                2                                            ⁢                                              ω                        4                                                              ]                                                        1                    2                                                                                                          K              2                        +                                                                                A                    4                                    ⁡                                      (                                                                  C                        ⁢                                                                                                  ⁢                        1                                            +                                              C                        ⁢                                                                                                  ⁢                        2                                            +                                              C                        ⁢                                                                                                  ⁢                        3                                                              )                                                  2                            ⁢                              ω                2                                                                        (        2        )            
On the basis of the above equations, a frequency characteristic of the transfer function of the differential pressure P relative to the flow rate Q in this shock absorbing device is as shown by a Bode diagram in FIG. 12. A transfer gain has Fa=K/{2×π×A2×(C1+C2+C3)} and Fb=K/{2×π×A2×(C2+C3)} as crossover frequencies, varies so as to be substantially C1 in a region where F<Fa and decrease gradually from C1 to C1×(C2+C3)/(C1+C2+C3) in a region where Fa≦F≦Fb, and is constant in a region where F>Fb. In other words, the frequency characteristic of the transfer function of the differential pressure P relative to the flow rate Q is such that the transfer gain increases in a low frequency region and decreases in a high frequency region.
Hence, in this shock absorbing device, as shown by a damping characteristic in FIG. 13, a large damping force can be generated in response to the input of low frequency vibration, and a small damping force can be generated in response to the input of high frequency vibration. Therefore, in a situation where the input vibration frequency is low, such as when a vehicle turns, a high damping force can be generated reliably, and in a situation where the input vibration frequency is high, such as when the vehicle travels on an irregular road surface, a low damping force can be generated reliably. As a result, an improvement in passenger comfort can be obtained in the vehicle.